A line is perpendicular to a line with slope -1/2. What is the slope of the perpendicular line?

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Multiple Choice

A line is perpendicular to a line with slope -1/2. What is the slope of the perpendicular line?

Explanation:
Perpendicular lines have slopes that are negative reciprocals of each other, so their product is -1. If one slope is -1/2, the other slope m must satisfy (-1/2)·m = -1. Solving gives m = 2. Quick check: the reciprocal of -1/2 is -2, and changing the sign gives 2, which matches. Using the other options would not yield a product of -1 (for example, -2 gives 1, 1/2 gives -1/4, and 0 would be horizontal). Therefore, the slope of the perpendicular line is 2.

Perpendicular lines have slopes that are negative reciprocals of each other, so their product is -1. If one slope is -1/2, the other slope m must satisfy (-1/2)·m = -1. Solving gives m = 2. Quick check: the reciprocal of -1/2 is -2, and changing the sign gives 2, which matches. Using the other options would not yield a product of -1 (for example, -2 gives 1, 1/2 gives -1/4, and 0 would be horizontal). Therefore, the slope of the perpendicular line is 2.

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